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More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics.…
This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…
By using the maximum entropy principle, with Tsallis entropy, we obtain an explicit dependence for energy distribution of earthquakes. This function describes very well the observations in a wide range of energies, where other distribution…
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…
A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as…
Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis…
Tsallis entropy is a generalized diversity index first derived in Patil and Taillie (1982) and then rediscovered in community ecology by Keylock (2005). Bayesian nonparametric estimation of Shannon entropy and Simpson's diversity under…
We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem…
We study the evolution of Tsallis entropy along the heat flow and establish its concavity in arbitrary dimensions. Extending prior results that were restricted to the one-dimensional setting, we prove that the Tsallis entropy is concave in…
How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the $complex$ of the complex networks. In this paper, a new method which is based on the Tsallis…
We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
In an earlier study, we showed that Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to non-extensive systems, can be used as a possible risk measure in constructing risk optimal…
In this paper, we investigate the partition inequality, joint convexity, and Pinsker's inequality, for a divergence that generalizes the Tsallis Relative Entropy and Kullback-Leibler divergence. The generalized divergence is defined in…
We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show…
The quantum relative Renyi entropy of two density matrices was recently extended when the two do not commute, from which a conditional entropy is identified. This is here extended to the corresponding Tsallis relative entropy and to its…
In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…
We propose a one-parameter family \ $\mathbb{R}_q$ \ of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the…
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…